Iraq's Sunni bloc has demanded greater concessions from its political rivals following PM Nouri al-Maliki's resignation.

Baghdad, Iraq - The resignation of Iraq's Prime Minister Nouri al-Maliki after a tense standoff has cleared the way for his replacement, Hayder al-Abadi, to attempt to bridge the gaps between Sunni and Shia leaders over the formation of a new government, according to Iraqi lawmakers.

Maliki's State of Law coalition won the most seats in April's parliamentary election, and Maliki had insisted on his right to form a government. But he came under intense pressure both from within his own party and internationally to step down after eight years in office.

The appointment of Abadi drew widespread support within Iraq, as well as from the United States and Iran. The parliament in Baghdad will now hold talks to form a new government. Under the Iraqi constitution, the Shia National Alliance (NA), which is the biggest bloc in parliament, has the exclusive right to form the government.

"The National Alliance will lead the talks with respect to [distributing] ministries, posts and the governmental programme, so Kurds and Sunnis have to deal with the NA," said Abdulkareem al-Anazi, a senior Shia lawmaker and a leader of NA.

"The problem is the governmental programme, which will include many tangles that the prime minister cannot deal with if he is not backed by all the Shia parties."

Whatever its make-up, Iraq's new government will face several serious challenges. Fighters from the Islamic State group now control large swathes of northwest Iraq after taking over the city of Mosul on June 10, and are fighting Kurdish forces who are now backed by limited US air support.

Tribal leaders and clerics from Iraq's Sunni heartland, where an uprising began in April 2013 after security forces launched a bloody crackdown on protests against Maliki's government, have said they would be willing to join the new administration, but that the government must first release thousands of Sunnis who have been held in prison for years without charge.

Iraqi Sunnis open to backing new PM.

Sunnis also are demanding the annulment of a controversial anti-terrorism law and the Justice and Accountability law, better known as the de-Baathification law, which was intended to outlaw elements of Saddam Hussein's Baathist regime. Sunnis allege that the law has been used to discriminate against them.

Meanwhile, the country's Kurds, who have run an autonomous region in Iraq's northeast since 1991, have extended their control over the oil-rich city of Kirkuk and other areas that have been under dispute with Baghdad.

"How will the new prime minister deal with Kurds with regards to Kirkuk and the disputed areas, and how will he react relating to the Sunni demands, if they insist to cancel the de-Baathification law, if he is not backed by a unified and strong bloc?" said a senior Shia negotiator, who spoke to Al Jazeera on condition of anonymity.

"The new prime minister will be backed by the National Alliance and this will reduce the demands of the other blocs," the official said.

Sunni and Kurdish blocs have been playing on the divisions between the Shia parties in an effort to get more concessions from Abadi, as he would be in a weaker position if the Shia National Alliance remains divided, Sunni politicians said.

"Many of the Sunni blocs see what happened as a disappointing situation. Dawa party leaders played a bypass movement to get Abadi back to the embrace of Dawa," said a senior Sunni politician, who spoke on condition of anonymity.

"Nominating Abadi away from Maliki's State of Law bloc was a typical way to get rid of the Dawa party's domination of the government."

Iraq is facing its most serious security challenge since a peak in sectarian bloodshed in 2006-2007. Fighters led by the Islamic State group have been overrunning many towns and cities in the west and north, forcing hundreds of thousands to flee their homes.

All Sunni parties know that any government, regardless of its power or the support that it has, has to rely on the Sunni parties or figures in these areas to form a local army to fight [the Islamic State group] and liberate their areas.

- Salah al-Joubori, Sunni lawmaker

Sunni politicians have said that any government would not be able to regain control over Iraq's Sunni provinces that have been overrun by Islamic State fighters without cooperating with local Sunni leaders.

"All Sunni parties know that any government, regardless of its power or the support that it has, has to rely on the Sunni parties or figures in these areas to form a local army to fight [the Islamic State group] and liberate their areas," said Salah al-Joubori, a Sunni lawmaker.

Sunnis, who say they have been marginalised by Maliki's government since 2006, said that as they are guaranteed a certain number of ministerial posts in Iraq's new power-sharing agreement, their priority will be political reform and long-held Sunni demands.

Sunni blocs in the parliament have decided to negotiate with the National Alliance as a single bloc. Sunni negotiators said their demands include amnesty for Sunni detainees, the immediate release of those who have not been convicted of a crime, and a resolution to the charges against Sunni leaders, including Rafie al-Essawi, the former Iraqi Finance Minister, and Ahmed al-Alwani, a prominent Sunni leader and a former lawmaker, who Maliki's government had accused of terrorism.

Joubori and several other Sunni lawmakers said that Sunnis expected the new government to be more flexible and open to Sunni demands than the previous one. "Abadi has got great international and regional support and he will not risk this support by being inflexible," said a senior Sunni leader, who declined to be named.

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